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Orion1

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Everything posted by Orion1

  1. If the computer is evaluating pi from scratch, such as the case example for the Atn(x) and partial sum functions, then the computer does not know that the answer is pi, so how can it 'know' to round up to the nearest decimal point? and in the case where the solution is only 3.141 at that point in the sum, then there are no further decimal places to round up from!.
  2. [math]4 \sum_{n=0}^{1687} \frac{(-1)^n}{2n+1} = 3.141... \; \; \; l = 4[/math] According to my computer algorithm and Mathematica and Wolframalpha, the solution is 3.141. Can anyone else verify? Reference: Wolframalpha - sum formula
  3. [math]\pi = 4 \sum_{n=0}^{\infty} \frac{(-1)^n}{2n+1}[/math] I calculated the integer sum steps required to complete each numerical place, note that these numbers are fundamental to this equation and are independent of any computer specifications. (i.e. CPU, RAM, Memory, OS, basic language, etc.) Integer sum: [math]n \; ( \text{2}, \text{18}, \text{118}, \text{1687}, \text{10793}, \text{136120}, \text{1530011}, \text{18660287}, \text{155974698})[/math] Numerical place: [math]n_l \; (3,1,4,1,5,9,2,6,5)[/math] Numerical length: [math]l \; (1,2,3,4,5,6,7,8,9)[/math] Example: [math]4 \sum_{n=0}^{1687} \frac{(-1)^n}{2n+1} = 3.141... \; \; \; l = 4[/math] Note that [math]l = 9[/math] required a compiler.
  4. [math]4 \cdot \sum_{n=0}^\infty \frac {(-1)^n} {2n+1} = \pi[/math] This equation appears to be the most reduced, however the arctan identity is gone.
  5. This simple trigonometry equation trumps all the hyperbole calculus equations stated on this thread so far. Calculation for pi: [math]4 \cdot \arctan(1) = \pi[/math]
  6. My calculation for the Higgs boson mass for the Standard Model. The Higgs boson mass is equal to one-half the Higgs vacuum expectation value. Higgs boson mass: [math]m_H = \frac{v_h}{2} = \frac{1}{2} \sqrt{\frac{(\hbar c)^3}{\sqrt{2} G_F}} = 123.111 \; \frac{\text{Gev}}{\text{c}^2}[/math] [math]\boxed{m_H = \frac{1}{2} \sqrt{\frac{(\hbar c)^3}{\sqrt{2} G_F}}}[/math] CERN Higgs boson mass: [math]m_H = 125.3 \pm 0.6 \; \frac{\text{Gev}}{\text{c}^2}[/math] Which implies that the Higgs boson achieves mass from the Higgs field vacuum via the Higgs mechanism. Reference: Physical constants - Wikipedia Higgs boson - Wikipedia Higgs mechanism - Wikipedia Higgs vacuum expectation value - Wikipedia Vector Boson Decay - ATLAS
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